Plan ahead for the next school year. Schedule your class today!

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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Jul 1, 2025
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
and train with the best! Please note that early bird pricing ends August 19th!
Are you tired of the heat and thinking about Fall? You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US.

Our full course list for upcoming classes is below:
All classes start 7:30pm ET/4:30pm PT unless otherwise noted.

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0 replies
jwelsh
Jul 1, 2025
0 replies
Random but useful theorems
booking   74
N 3 minutes ago by drazirahc
There have been all these random but useful theorems
Please post any theorems you know, random or not, but please say whether they are random or not.
I'll start give an example:
Random
I am just looking for some theorems to study.
74 replies
booking
Jul 16, 2025
drazirahc
3 minutes ago
9 Mixed numbers
GA34-261   127
N an hour ago by phoenix999
personally i hate mixed numbers. they're rarely used in competition math and just don't make sense unless you want to estimate a value. i hate how in school they make you "simplify" everything into a mixed number or else it's wrong :(
127 replies
GA34-261
Jun 3, 2025
phoenix999
an hour ago
9 Easiest math competition
a.zvezda   55
N 2 hours ago by phoenix999
MOEMS, Math Kangaroo, and Beestar are to me the easiest. :P
55 replies
a.zvezda
Jul 15, 2025
phoenix999
2 hours ago
The 24 Game, but with a twist!
PikaPika999   423
N 3 hours ago by AgileMongoose21
So many people know the 24 game, where you try to create the number 24 from using other numbers, but here's a twist:

You can only use the number 24 (up to 5 times) to try to make other numbers :)

the limit is 5 times because then people could just do $\frac{24}{24}+\frac{24}{24}+\frac{24}{24}+...$ and so on to create any number!

honestly, I feel like with only addition, subtraction, multiplication, and division, you can't get pretty far with this, so you can use any mathematical operations!

Banned functions
423 replies
PikaPika999
Jul 1, 2025
AgileMongoose21
3 hours ago
No more topics!
9 Favorite topic
A7456321   249
N Jul 17, 2025 by BrilliantScorpion85
What is your favorite math topic/subject?

If you don't know why you are here, go binge watch something!

If you forgot why you are here, go to a hospital! :)

If you know why you are here and have voted, maybe say why you picked the option that you picked in a response) :thumbup:

CLICK ON ME YOU KNOW YOU WANT TO

Timeline
249 replies
A7456321
May 23, 2025
BrilliantScorpion85
Jul 17, 2025
Favorite topic
G H J
G H BBookmark kLocked kLocked NReply
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skronkmonster
2226 posts
#240 • 3 Y
Y by GA34-261, PikaPika999, A7456321
Probably CP (and maybe geometry). Surprised there aren't more votes for CP in the poll honestly, but I guess a lot of people like algebra as well
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Kushagra2012
21 posts
#241 • 3 Y
Y by PikaPika999, GA34-261, A7456321
The voting percentage of "Arithmetic" is very very low.
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tintin21
1115 posts
#242 • 4 Y
Y by PikaPika999, Sushi_Academy, GA34-261, A7456321
Kushagra2012 wrote:
The voting percentage of "Arithmetic" is very very low.

this might be just me but, arithmetic is pretty much the most boring topic in math if you can count it as one
EDIT: 1100 post! :first:
This post has been edited 1 time. Last edited by tintin21, Jul 15, 2025, 6:18 PM
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PikaPika999
3709 posts
#243 • 2 Y
Y by GA34-261, A7456321
Inaaya wrote:
PikaPika999 wrote:
emilyn776 wrote:
Algebra. It's fun, logical, doesn't need you to bang your head against ten different walls - okay sometimes it does - but I just enjoy it since it feels like you're solving something rather than just doing math.

you don't need to bang your head on 10 different walls. You need to bang your head on 11 different walls
actually it requires banging your head on the square root of negative i walls

:stretcher: wait wat
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sanaops9
864 posts
#244 • 3 Y
Y by PikaPika999, GA34-261, A7456321
mpcnotnpc wrote:
@2above
that's wrong btw

Wait how, I might be blind
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Inaaya
498 posts
#245 • 3 Y
Y by GA34-261, PikaPika999, A7456321
PikaPika999 wrote:
Inaaya wrote:
PikaPika999 wrote:

you don't need to bang your head on 10 different walls. You need to bang your head on 11 different walls
actually it requires banging your head on the square root of negative i walls

:stretcher: wait wat
chat what is the square root of negative i
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giratina3
660 posts
#246 • 3 Y
Y by GA34-261, PikaPika999, A7456321
For @2above

I find nothing wrong with the answer. It's just the 12th roots of unity.
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skronkmonster
2226 posts
#247 • 3 Y
Y by GA34-261, PikaPika999, A7456321
Kushagra2012 wrote:
The voting percentage of "Arithmetic" is very very low.

it's boring, but those who make silly mistakes a lot would probably hate "Arithmetic"
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PikaPika999
3709 posts
#248 • 1 Y
Y by A7456321
Inaaya wrote:
chat what is the square root of negative i

apparently $\sqrt{i}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}i}{2}$ but idk
This post has been edited 1 time. Last edited by PikaPika999, Jul 16, 2025, 4:27 PM
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giratina3
660 posts
#249 • 2 Y
Y by PikaPika999, A7456321
PikaPika999 wrote:
apparently $\sqrt{i}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}i}{2}$ but idk

@OP meant negative $i$
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Aaronjudgeisgoat
938 posts
#250 • 2 Y
Y by PikaPika999, A7456321
Inaaya wrote:
chat what is the square root of negative i

-i can be written as (1, 270) in polar so the two square roots are (1, 135) and (1, 315) which in cartesian turns out to be $\frac{-\sqrt2}{2}+\frac{\sqrt2}{2}i,$ and the negation of that. obviously, there is no concept of "positive" with complex numbers so u dont know which one is the positive square root
This post has been edited 1 time. Last edited by Aaronjudgeisgoat, Jul 16, 2025, 7:22 PM
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NoodlesSKY
284 posts
#251 • 2 Y
Y by PikaPika999, A7456321
geometry ftw
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PikaPika999
3709 posts
#252 • 1 Y
Y by A7456321
giratina3 wrote:
PikaPika999 wrote:
apparently $\sqrt{i}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}i}{2}$ but idk

@OP meant negative $i$

yes, and you need to know the square root of i to find the square root of negative i.

just multiply the square root of i by i
This post has been edited 1 time. Last edited by PikaPika999, Jul 17, 2025, 4:23 PM
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b2025tyx
1492 posts
#253 • 2 Y
Y by PikaPika999, A7456321
is there an option for everything?
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BrilliantScorpion85
92 posts
#254 • 2 Y
Y by PikaPika999, A7456321
yeah probably
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